Suppose that the functions and are defined for all real numbers as follows.

Write the expressions for and and evaluate .

For the given recursive formula of the sequence , the value of A₈ = -17.

As given in the question,

Recursive formula of the sequence is given by,

Aₙ = 2Aₙ₋₁  - 3Aₙ₋₂

And the value of

A₁ = -1 , A₂ = 1

Substitute the n = 3 , 4, 5, 6, 7, 8  in the recursive formula to get the value of A₈ we have,  

A₃ = 2A₂ - 3A₁

    = 2(1) -3(-1)

    = 5

A₄= 2A₃ - 3A₂

    = 2(5) - 3(1)

    = 7

A₅ = 2A₄ - 3A₃

    = 2(7) - 3(5)

    = -1

A₆ = 2A₅ - 3A₄

    = 2(-1) - 3(7)

    = -23

A₇ = 2A₆ - 3A₅

   = 2(-23) - 3(-1)

   = -43

A₈ = 2A₇ - 3A₆

    = 2(-43) - 3(-23)

    = -17

Therefore, for the given recursive formula of the sequence , the value of A₈ = -17.

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Answer:

It is the method by multiplication

Step-by-step explanation:

5×5=25

[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill & 2\\ P=\textit{initial amount}\dotfill &18\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years \end{cases}[/tex]

[tex]2=18(1 - 0.04)^{t}\implies \cfrac{2}{18}=(1 - 0.04)^{t}\implies \cfrac{1}{9}=0.96^t \\\\\\ \log\left(\cfrac{1}{9} \right)=\log(0.96^t)\implies \log\left(\cfrac{1}{9} \right)=t\log(0.96) \\\\\\ \cfrac{\log\left(\frac{1}{9} \right)}{ ~~ \log(0.96) ~~ }=t\implies 53.82\approx t\qquad \textit{about 53 years and 301 days}[/tex]

It will take approximately 54 years for the element to decay from 18 grams to 2 grams at a rate of 4% per year.

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

To determine how long it takes for an element to decay from 18 grams to 2 grams, you can use the formula:

t = (ln(A/B)) / (-r)

where:

t is the time it takes for the decay to occur

A is the initial amount of the element, in this case 18 grams

B is the final amount of the element, in this case 2 grams

r is the decay rate, in this case 4% per year

Plugging these values into the formula gives you:

t = (ln(18/2)) / (-0.04)

t = (ln(9)) / (-0.04)

t = (2.1972) / (-0.04)

t = -54.30

Hence, It will take approximately 54 years.

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Answer:

  f(x) = 3(x +1)² +2

Step-by-step explanation:

You want the equation in vertex form of the parabola 3x² after its vertex is translated to (-1, 2).

The given form is the "vertex form" of the equation for a parabola. That is, in the form ...

  f(x) = a(x -h)² +k

the value of 'a' is the leading coefficient, the scale factor, and the values of h and k are the x- and y-coordinates of the vertex.

Given that the scale factor of the desired parabola is a=3, and the desired vertex is (h, k) = (-1, 2). we can fill in these values in the equation to get ...

  f(x) = 3(x -(-1))² +2

  f(x) = 3(x +1)² +2

[tex]2x+y+3\sqrt 5=0[/tex]

​

Step-by-step explanation:

hope this helped

Answer:

-5/4

Step-by-step explanation:

Step 1: Convert to algebraic equation.

4x +7 = 2

Step 1: Subtract 7 from both sides.

4x +7 −7 = 2 −7

Step 2: Divide both sides by 4.

(4x /4) = (-5 /4)

Step 3: Get your answer!

x = -5/4

Answer:

x = -1.25

Step-by-step explanation:

A number = x

7 + 4x = 2

Subtract 7 on both sides

4x = -5

Divide both sides by 4

x = -1.25 OR -5/4

The value at which acceleration is zero is t = 5/3

Acceleration is defined as the rate at which velocity changes with time, in terms of both speed and direction

Given: the equation of motion, velocity, s = t⁶ - 2t⁵

Since acceleration is the rate at which velocity changes with time.  You need to differentiate the velocity with respect to time. Thus:

ds/dt = 6t⁵ - 10t⁴                  (Note: ds/dt is the acceleration)

Also, acceleration is equal to zero. That is:

6t⁵ - 10t⁴ = 0

6t⁵ = 10t⁴

6t = 10

t = 10/6 = 5/3

Therefore, the value of t at which acceleration is zero is t = 5/3

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The distance between the points, (-8, -2) and (12, 10), is 23.3

From the question, we are to determine the distance between the two given points.

From the given information,

The points are (-8, -2) and (12, 10)

The distance between two points in given by the formula

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where d is the d is the distance between the points

Thus,

d = √[(12 - (-8))² + (10 - (-2))²]

d = √[(12 + 8)² + (10 + 2)²]

d = √[(20)² + (12)²]

d = √[400 + 144]

d = √[544]

d = 23.3

Hence, the distance is 23.3

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The probability that their babies would have brown wool will be 25%.

When two or more alleles for the same characters are present at the same loci on homologous chromosomes, a cell, a nucleus, or a single organism is said to be heterozygous. In contrast to homozygous, where the alleles are identical, it signifies that the alleles that code for the same gene or characteristic are different.

Given, the two-parent sheep would need to have heterozygosity for their genotype if we were to assume straightforward Mendelian genetics. Black would not be dominant in this situation; instead, the parents would be, shall we say, Rr for color. Imagine that each parent can only contribute one allele (either the R or the r). If both should chance to deliver the r, the child would be black.

Therefore, 25% of the following generation's children are likely to be black. There would be a 25% probability of a homozygous dominant offspring, a 50% chance of a heterozygous offspring, and a 25% chance of a homozygous recessive offspring if you filled out a Punnett square for this issue. Since white is the dominant allele in this situation, both the homozygous dominant allele, which accounts for 75% of the possibilities and the heterozygous child will be white. Since two recessive alleles are required to manifest the recessive phenotype, the remaining 25% of people are black.

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∠G+∠H+∠J=180 and ∠K+∠L+∠M=180 from the angle sum property of triangle, ∠H=∠L (3rd Angle Theorem) and ∆GHJ≅∆KLM from ASA congruency theorem.

In the given question we have to prove ∆GHJ congrurnce ∆KLM.

Given that: ∠G≅∠K, ∠J≅∠M, [tex]\over{HJ}[/tex] ≅ [tex]\over{LM}[/tex].

As given that;

∠G≅∠K

∠J≅∠M

[tex]\over{HJ}[/tex] ≅ [tex]\over{LM}[/tex]

So from the angle sum property of triangle

∠G+∠H+∠J=180................(1)

∠K+∠L+∠M=180.................(2)

Now equation equation 1 and 2

∠G+∠H+∠J=∠K+∠L+∠M

As we know that ∠G=∠K, ∠J=∠M

So now the expression is

∠G+∠H+∠J=∠G+∠L+∠J

After solving ∠H=∠L (3rd Angle Theorem)

Since, ∠H=∠L, HJ=LM and ∠G=∠K, so from the theorem Angle Side Angle(ASA) congruency,

∆GHJ≅∆KLM

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Answer:

negative x over 4 + three-fourths = 12

Answer:

Step-by-step explanation:

(StartFraction negative x over 4 EndFraction + three-fourths = 12

The function that could be used to represent the total cost of the shoes by applying the $15 coupon first and the 20% member discount second for original cost, using proportions, is of:

C(x) = 0.8(x - 15).

A proportion represents a fraction relative to a total amount, and this fraction is combined with the basic arithmetic operations, especially division and multiplication, to find the desired amounts in whichever context of the problem.

The value of shoe is given as follows:

x.

The discounts are given as follows:

Hence the function that gives the total cost paid is presented as follows:

C(x) = 0.8(x - 15).

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Answer:

Step-by-step explanation:

{x,y}={0,-3}

Answer:

x-3

Step-by-step explanation:

2x²-6x=0

divide both sides by x

2x²/x -6x/x=0

2x-6=0

2x=6

x=6/2

x=3

or (x-3)

Answer:

All you simply do is divide 23,500 by 500....that is equal to 47. So 47 is the answer

Step-by-step explanation:To find out how many reams were used, all we have to do is divide 23,500 by 500.

This gives us: 47 reams

The system of equations are graphed in the image below, showing that they have infinitely many solutions, which include (3, 0) and (0, 3).

The values of a pair of x and y that will make two different equations in a system true is the solution to the system of equations.

By graphing, we can determine the solution by finding the x and y coordinates of the point that both lines of the equations intersect at.

The lines of x + y = 3 and 5x + 5y = 15 are graphed in the image below, which is the same blue line. This shows that the equations have infinitely many solutions such as (3, 0) and (0, 3).

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The bicycle wheel performs 10 revolutions every minute

A revolution in math is a full rotation, or a complete, 360-degree turn. In a 360-degree rotation, the object starts and ends in the same position. A mathematical revolution can be visualized when a top spins.

The bicycle wheel makes 1 complete revolution which is equal to the circumference of the wheel = πD

but D =  diameter = 42 inches, converting inches to feet

12inches is 1 foot, then 42 inches = 42/12 = 7/2 inches

Also circumference = 22/7 x 7/2 = 11 feet/rev

Also if the rider travelled 110 feet per minute.

Then the wheel's revolution per minute = 110/11
                                                                   = 10 rev/minute

In conclusion the bicycle wheel revolves 10 times every minute

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Using prime factorization to rewrite 156 +36 as a product of the GCF and a sum of numbers will be 12(13 + 3).

Prime factorization simply means the process of writing all numbers based on the product of their prime.

In this case, it's important to note that:

156 = 13 × 12

36 = 3 × 12

Therefore, 156 + 36 will be:

= 12(13 + 3)

This illustrates the numbers.

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During the progressive era many state and local governments adopted initiative referendum and recall together these procedures gave citizens a more direct voice in government.

At the progressive era the citizens was given by a more direct voice in government because of the three principles they are initiative ,referendum and recall.

Initiative:

Proposed law with backing can be put on the ballot at election,in that case the petitions must be approved with valid signatures.

Referendum:

plebiscite is a kind of referendum in which meaning decree of the people it depends on nature of advisory called as referendum.

Recall:

Recall defines that voters may remove a public official from office that must be before the expiration.

Therefore During the progressive era many state and local governments adopted initiative referendum and recall together these procedures gave citizens a more direct voice in government.

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Answer:

9: 71 , 10: 110, 11: 52

Step-by-step explanation:

the sum of angles in a triangel is 180°

so for 9:

180 = 78 + 31 + x

180 - 78 - 31 = x = 71

it's a sharp triangel because all angles are smaller than 90°

you can calculate the angles of 10 and 11 the same way

which gives 10: 110°

this is a stump triangel because there s an angle greater than 90°

The last one is a right triangel because it has a 90° angle (marked with the square)

The number of ways to select the banners is given as follows:

a. Matching with the country: 362,880.

b. Not matching with the country: 60,949,324,800

To select the banners matching the country, only the nine countries are chosen, and then the specific banner regarding the country is chosen, thus the arrangements formula is used.

The number of possible arrangements of n elements is given by the factorial of n, that is:

[tex]A_n = n![/tex]

Hence for item a the total number of outcomes is the factorial of nine, which is the number of countries, is given as follows:

Total = 9! = 362,880.

Then just nine banners are taken at random from a set of 20. The order is important, hence the permutation formula is used.

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this problem, 9 banners are selected from a set of 20, hence the number of ways is:

N = 20!/(20 - 9)! = 20!/11! = 60,949,324,800.

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For the given defined function f(x) for all real numbers , value of required function are as follow:

f(-1)  = -2 , f(2) = 4 and f(5) = -1.

As given in the question,

Function is defined as follow for all the real numbers,

f( x ) = -2  , if x ≠ 2

f(x) = 4 , if x =2

Values of the required function is given by :

f ( -1 )  for the required function x = -1 which is not equal to 2.

Hence , f( -1 ) = -2

f ( 2 )  for the required function x = 2 which is equal to 2.

Hence , f( 2 ) = 4

f ( 5 )  for the required function x = 5 which is not equal to 2.

Hence , f(5 ) = 4.

Therefore, for the given defined function f(x) for all real numbers , value of required function are as follow:

f(-1)  = -2 , f(2) = 4 and f(5) = -1.

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The percentage reduction of the jacket is 20 percent.

Percentage decrease or reduction means subtracting a given percentage of a value from the original value.

Therefore, the jacket cost 80 dollars and it is reduced to 64 dollars.

The percentage reduction of the jacket can be calculated as follows:

% reduction = (Decreased Value / Original Value) × 100

Decreased value = 80 - 64 = 16

Original Value = 80

% reduction = 16 / 80 × 100

% reduction = 1600 / 80

% reduction = 20%

Therefore, the percentage reduction is 20%.

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The equation of line that is perpendicular to the line y = 1/2x + 2 is y = -2x - 7

A perpendicular line is a straight line through a point. It makes an angle of 90 degrees with a particular point through which the line passes. Coordinates and line equation is the prerequisite to finding out the perpendicular line.

The equation of perpendicular line is given as

(y - y₁) = m(x - x₁)

m = slope of the line.

But the slope of a perpendicular line is given as

m₁m₂ = -1

m₁ = 1/2, m₂ = ?

1/2m₂ = -1

m₂ = -2

The new slope is -2.

Substituting the values into the equation above,

(y - y₁) = m(x - x₁)

y - 1 = -2(x - (-4))

y - 1 = -2x - 8

y = -2x - 7

The new equation is y = -2x - 7

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Answer:

1,265

Step-by-step explanation:

10^3=1000*2=2000

105*7=735

2000-735

Answer:

∠W = 36.6°

Step-by-step explanation:

Hello!

If angles are complementary, it means that they add up to 90°.

Since the measure of Angle X is 53.4, we can find measure of Angle W by subtracting 53.4 from 90.

The value of W is 36.6°.